N-Fold compound option pricing with technical risk under fractional jump-diffusion model

Abstract

The problem of generalizing the compound option pricing model to incorporate more empirical features becomes an urgent and necessary event. In this study, a new N-fold compound option pricing method is designed for the economic uncertainty and technical uncertainty. The economic uncertainty is modelled by a fractional jump-diffusion model, which incorporates the long-term dependence of financial markets, the kurtosis of returns and the unpredictable shocks of real world. The technical uncertainty is modelled as a simplified version Poisson-type jump process, which describes the catastrophic impact of the technical risk in multi-stage projects. The main contribution of this paper is that we firstly develop the N-fold compound option pricing model with the fractional Brownian motion and the technical risk variable. Further, the analytic solutions of pricing compound options are achieved and verified by the recursive formula of option price. Numerical examples are provided to support the theoretical results of this model. Moreover, from the sensitivity analysis, some results are presented to illustrate that the N-fold compound option price without considering the phase-specific characteristics of technical risk is improperly estimated. Thereby, it is essential for investors to take into account the technical risk when making decisions.